Hydrological infrastructure such as pumps and floodgates are invaluable assets for mitigating flooding in coastal cities. These infrastructure components are often vulnerable to damage or failure due to the impact of flood waters, thus exacerbating the flood hazards and causing significant loss of life and destruction to property worth billions of dollars. Hence, there is a growing need worldwide to enhance the understanding of flood vulnerability and to develop key metrics for assessing it. This study proposes an approach for measuring the vulnerability of hydrological infrastructure to flood damage in coastal cities. In this approach, a hydrological infrastructure flood vulnerability index (HIFVI) is developed based on exposure, sensitivity and resilience of infrastructure assets to flooding. A graph-theoretic algorithm for implementing the proposed HIFVI is presented and applied to assess the flood vulnerability of floodgates in one of the most representative coastal cities - Jakarta, Indonesia. The application involves the construction of a graph-based spatio-topological network model of Jakarta's hydrological system, with floodgates represented as network nodes and waterways as edges. An analysis of the constructed network is carried out based on the underlying graph-theoretic algorithm to compute HIFVI for all nodes that represent floodgates. The results show that HIFVI can point to the most vulnerable hydrological infrastructure components and also highlight locations within coastal cities where additional infrastructure are required to improve resilience to flooding. These information are vital to decision makers when planning and prioritising infrastructure maintenance and resource allocation for flood preparedness in coastal cities.